Geodesic
Orthogonal Solutions for a Hyperbolic System
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 125-130.

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We consider the hyperbolic system $$ \begin{cases} u_t=a\nabla v+f_1(u,н)\\ v_t=a\nabla u+f_2(u,н)\\ u(0,x)=\xi(x)\\ v(0,x)=\eta(x), \end{cases} $$ and we are looking for necessary and sufficient conditions on the forcing terms $f_i$, $i=1,2$, in order that the semigroup solutions, $u$ and $н$, starting from orthogonal data $\xi,\eta\in L^2(\mathbb R^n)$, remain orthogonal on $\mathbb R_+$. 
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Ovidiu Cârjă; Mihai Necula; Ioan I. Vrabie. Orthogonal Solutions for a Hyperbolic System. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 125-130. http://geodesic.mathdoc.fr/item/BASM_2008_1_a6/

[1] Bouligand H., “Sur les surfaces dépourvues de points hyperlimités”, Ann. Soc. Polon. Math., 9 (1930), 32–41

[2] Burlică M., Roşu D., “A viability result for semilinear reaction-diffusion systems”, Proceedings of the International Conference of Applied Analysis and Differential Equations (4–9 September 2006, Iaşi, Romania), eds. O. Cârjă and I. I. Vrabie, World Scientific, 2007, 31–44 | MR

[3] Cârjă O., Motreanu D., “Flow-invariance and Lyapunov pairs”, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13B, suppl. (2006), 185–198 | MR

[4] Nagumo M., “Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen”, Proc. Phys.-Math. Soc. Japan, 24 (1942), 551–559 | MR | Zbl

[5] Pavel N. H., “Invariant sets for a class of semi-linear equations of evolution”, Nonlinear Anal., 1:2 (1976/1977), 187–196 | DOI | MR

[6] Severi F., “Su alcune questioni di topologia infinitesimale”, Annales Soc. Polonaise, 9 (1931), 97–108 | Zbl

[7] Vrabie I. I., $C_0$-Semigroups and Applications, North-Holland Mathematics Studies, 191, Elsevier, 2003 | MR